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All IPCC definitions taken from Climate Change 2007: The Physical Science Basis. Working Group I Contribution to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, Annex I, Glossary, pp. 941-954. Cambridge University Press.

Posted on 29 February 2012 by Tom Curtis

Heating and Heat Flow

Some physics, everyone knows. In our daily lives we encounter the effects of physics all the time, and as a result, we know what physics predicts in those circumstances at a gut level. We may not be able to put it into numbers. We may not be able to apply it in novel situations. But we know it all the same.

One example is as simple as putting on a blanket. We know that if we want warm something up, we can increase the supply of heat - or we can reduce the escape of heat. Either is effective. If you have a pot that is simmering and you want to bring it to the boil, you can turn the heat up, or you can put on the lid. If we put on the lid, the pot will go nicely from simmering to boiling, and we don't need to turn up the heat even slightly. Indeed, if we are not careful to turn down the heat, the pot may well boil over.

Likewise, if you have two identical motors running with an identical load and speed (Revolutions Per Minute), one with the water pump working and one without, we are all physicist enough to say that the second one will run hotter. It does not matter that the energy supplied as fuel is identical in both cases. The fact that heat escapes more easilly with water circulating through the radiator will keep the first cooler. The consequence is that stopping the the water from circulating will lead second motor to disaster.

Nor do we find people who doubt this. Suppose somebody told us their water pump was broken, but that the Second Law of Thermodynamics prohibited transfer of heat from a cooler place (the water) to a hotter place (the engine block), so they'ld be fine so long as they didn't rev any faster than normal, we'ld look at them in complete disbelief. Or we would if we were too polite to burst out laughing. And if they set out cross country confident in their belief, it doesn't matter what destination they claim they're heading for. Rather, as we all know, they're really heading for a breakdown!

(Image copyright to iStock, and not to be reproduced without their permission.)

Heat Flow to Space

This physics that everyone knows is not only true of pots and radiators. It is true of the Earth as well. The Earth is warmed by our remarkably stable Sun. As a result, the Earth's surface radiates energy to space, and over time the incoming energy balances the outgoing energy. The process is made more complicated, however, by the existence of Infra Red (IR) absorbing molecules in the atmosphere.

Without those molecules, Infra Red radiation from the Earth's surface would travel directly to space, cooling the Earth quickly and efficiently. At certain wavelengths of Infra Red radiation, however, those molecules absorb many, or all, of the photons emitted from the Earth's surface. That energy is often redistributed among other molecules by collision, but eventually some of the redistributed energy will be reradiated by the Infra Red absorbing molecules. This process absorption, redistribution and then re-emission may occur many times before the energy escapes the atmosphere, but eventually it will either by being emitted to space, or back to the surface.

Intuitively, the energy that goes through multiple stages of absorption, redistribution and re-emission will not escape to space as fast that which is emitted directly to space from the surface. This intuition is sound, but it depends essentially on one factor, the temperature of the atmosphere.

We can see this by considering a fundamental law that governs the radiation of energy, the Stefan-Boltzmann Law:

In words, that is J-star equals epsilon sigma T to the fourth power, but we don't need to worry about that. What we need to notice is that J-star, which is the energy radiated over a given time from a given area, is proportional to the fourth power of T, ie, temperature. If the temperature doubles, the energy radiated increases sixteen-fold. If it triples, it increases eighty-one- fold. And so on. So, if the temperature of the atmosphere is different from that of the surface, the absorption, redistribution and re-emission of IR radiation by molecules in the atmosphere will certainly change the rate at which heat escapes to space.

Higher is Colder

There is another piece of physics everyone knows. It is that as you go higher in the atmosphere, the atmosphere gets colder. That is the reason why some mountain peaks are snow covered while their bases are still warm. This is not a universal law. It is not true, for example, in the stratosphere where the absorption of UltraViolet radiation from the Sun causes temperatures to rise with increased height. But eighty percent of the Earth's atmosphere is in the troposphere (the lowest layer of the Earth's atmosphere), and most radiation leaving the top of the troposphere escapes to space. And in the troposphere, as you get higher, the temperature gets lower. On average, the temperature drops by 6.5 degrees C for every thousand meters of altitude you climb. That means, for example, that the temperatures fall by about 24.5 degrees C as you climb to the summit of Mount Fuji, and by 50 to 100 degrees as you rise to the top of the troposphere.

We have already seen that temperature significantly effects the radiation of heat. Colder objects radiate less energy, and the Infra-Red absorbing molecules in the atmosphere are colder than the surface. Therefore it is no surprise that the Infra-Red absorbing molecules in the atmosphere radiate less energy to space than they absorb from the warmer surface. That difference is the essence of the greenhouse effect.

No More Arm Waving

It would be helpfull to recapitulate at this point. So far we have noted four simple facts:

That if you reduce the escape of heat, but do not reduce the incoming heat, things warm up;

That the atmosphere contains molecules that absorb Infra-Red radiation;

That radiated energy depends on the temperature of the radiating object; and

That the atmosphere gets cooler as you get higher, so that the Infra-Red absorbing molecules in the atmosphere radiate less energy to space than they absorb from the surface.

These four facts imply the existence of an atmospheric greenhouse effect, ie, that the presence of Infra-Red absorbing molecules in the atmosphere results in the surface being warmer than it otherwise would be.

In science, however, purely verbal reasoning like this is considered suspect. The reason is that sometimes odd effects occur that render verbal reasoning moot. So in science, there is no substitute for putting the theory into a mathematical form. It gets rid of the arm waving.

Fortunately for us, scientists have already put this theory into mathematical form, at a very detailed level. We can access this work, free of charge, by using the Modtran Model. The Modtran Model shows the radiation up or down over a column of atmosphere under particular conditions. By changing the conditions, you can explore the predicted effects of those changes on upward or downward radiation at any level of the atmosphere from 0 to 70 kilometers altitude. Setting the altitude to 70 kilometers effectively shows the radiation upward to space from the top of the atmosphere, or downward from space at the top of the atmosphere. Setting the altituded to 0 kilometers effectively shows the radiation upward, or downward at the surface.

Using Modtran, I determined the energy output looking downwards from an altitutude of 70 kilometers using the US Standard Atmosphere (1). The result can be seen on the following graph as the green shaded area. I repeated the model run, but this time with the altitude set at 0 km. The result is shown by the outer curve defining the red area in the graph below. That means that the red area itself, which is the upwards radiation from the surface minus the upward radiation to space, is the reduction in energy radiated to space because of the presence of Infra-Red absorbing molecules in the atmosphere. That is, it is the greenhouse effect.

Settled Science

We have all heard how inaccurate models can be. Therefore the fact that a particular model predicts this difference in radiation only shows what the theory predicts. It does not show what is actually happening.

Scientists are not happy with theories whose only support is a model. So in 1969, Conrath and associates compared the results of model calculations of radiation to space with the actually observed radiation using the IRIS instrument on the Nimbus 3 Satellite. The following graph shows the result of their comparison. The dotted line shows the modelled values, while the solid line shows the observed values:

The effect of a particular Infra-Red absorbing molecule, Carbon Dioxide, is clearly visible. With the publication of this data in 1970, the greenhouse effect ceased to be theoretical. It was an observed fact.

Comments

You are preaching to a very large choir. Very few people disagree that the green house effect operates and that doubling of CO2 ought to raise the temperature about 1.2°C. Here's what it says in Chapter 8 of the IPCC's AR4:

In the idealised situation that the climate response to a doubling of atmospheric CO2 consisted of a uniform temperature change only, with no feedbacks operating (but allowing for the enhanced radiative cooling resulting from the temperature increase), the global warming from GCMs would be around 1.2°C (Hansen et al., 1984; Bony et al., 2006).

Steve Case @1, I am glad that you are part of that very large choir, and hope you make sure you sing your part when that theory is challenged, as if frequently is, at WUWT and other so called "skeptic" sites. My experience has been, however, that even these basics are challenged frequently and vehemently by many so-called "skeptics", while others who should know better stand idly by, or egg them on.

You are preaching to a very large choir. Very few people disagree that the green house effect operates

Yes, very few people disagree with this. But unfortunately, they're represented in relatively high numbers in "skeptical" circles, which makes this post timely and necessary.

Personally, I've debated "skeptics" who didn't know that there's a difference in seasons between the northern and southern hemispheres, and who assumed that snow storms are basically impossible on a warming planet. I've also dealt with "skeptics" who assume that carbon dioxide can't affect the climate because it's heavier than oxygen. And believe it or not, they don't necessarily back off when you point out that atmospheric gases don't form layers based on weight, as evidenced by the fact that we haven't all been asphyxiated.

As we've seen again and again, this is what happens when a political movement exploits public ignorance for its own gain: After a while, no fact is too simple or obvious to require a clear explanation. That's why people on the scientific side of this argument have to work so much harder than "skeptics" who can spout any pseudoscientific gibberish that flatters people's prejudices.

Very few people don't believe in the greenhouse effect.
Very few people don't believe the earth is warming.
Very few people don't believe that fossil fuels are the cause.
Very few people don't believe warming will be bad.
Very few people don't believe feedbacks will make it worse.
Very few people don't believe that Arctic ice melt is related to warming.
Very few people don't believe that...

The list goes on and on. That's what is so wonderful about denial. There are so very many delicious flavors to choose from! And you can always couch your own particular passion with "well, yes, of course that's true, but..."

And so there is a very, very large denial choir, all singing different songs, out of tune, at the tops of their lungs, and it adds up to inaction and ignorance.

So every step along the way the most obvious things must be explained, as clearly and as simply as possible, so that bit by bit the cacophony of that very large and very diverse choir will slowly but surely, member by reluctant member, start to sing the same, harmonious song... and cut the crap and let us get on with the arduous task of fixing the problem rather than arguing about whether or not science is science.

Tom Curtis: Thanks for the very helpful information! A related point has been unclear to me for a long time and I wonder if you can clarify it for me.

Does the average altitude from which IR radiation is lost to space from the atmosphere depend on the concentration of greenhouse gases in the atmosphere? If so, then how does this affect the overall greenhouse process?

There were comments at this site some time ago (too long for me to find them now) that led me to believe that increasing the CO2 content of the atmosphere raises the average altitude from which IR radiation escaped to space. Ever since that time I have wondered how that works (if true), and your post has stimulated me to ask.
Thanks,
Bob

Steve Case: don't know if you challenge the accepted climate sensitivity, but denialists claims don't really know many boundaries. They freely wander from denying the warming, to denying the causes, to opposing the policies... and back step 1. One claim can be refuted, but moving goalposts are impossible to catch up with, specially in the attention span available from the broader audience.

Like the Denial Tango goes, "I'm skeptical of everything I just don't wanna know".

It was predicted that one of the fingerprints of climate change would be warming of the troposphere at around 10 km altitude. I did my own analysis a few years ago and showed that this was indeed the case.

boba: I believe that is the case. My crude explanation of the effect is that the increase in CO2 content increases the opacity of the whole column of gas. However the gas gets thinner as you go up, reducing the opacity.

At some point the opacity gets low enough that a good proportion of the IR photons can escape without further re-absorption. As the opacity of the whole column increases due to increasing CO2, that height gets higher.

I think it must be rather more complex than that though, because the emitted radiation higher up is at a lower temperature. Which means there are different number of photons being emitted in the transparent and opaque bands. I presume that codes like MODTRAN have to deal with that.

boba, Kevin C - As the effective emission altitude increases, and given that the lapse rate means cooler air at higher altitudes, the amount of energy radiated to space will (initially) decrease.

That means less energy leaving the atmosphere, and the climate warms. To a first order approximation, the atmosphere warms enough that the effective altitude is emitting same amount as the incoming energy - so it ends up near the same temperature (although pressure effects play into it as well), radiating away the same energy as before.

DrTsk - Given that the radius of the Earth is ~6350km, and changes in top of troposphere are <1km, effective area changes are a trivial influence. And more than balanced by the fact that lower pressure requires a slightly higher temperature (as there are fewer molecules) to emit the same energy.

Steve Case, so you accept the fundamentals of CO2 causing warming (which puts you in a different league to Yogi, who clearly does not think this), but you don't accept the feedbacks. Some reading for you, then. Read the following post, the sixteen peer-reviewed papers that are referenced therein, and the five linked blog posts with further references to the literature:Empirical evidence for positive feedback. If you doubt the evidence presented there, maybe you could comment over there as to why positive feedbacks don't exist. And also then give us your hypothesis as to how we had ice ages...

And Steve Case, perhaps you could educate GallopingCamel (comment #40 on this thread) as to the greenhouse effect operating. GC believes some crackpot theory about gravity he read on WUWT...

Very few people, indeed, disagree with the basic radiative forcing properties of CO2 that have been demonstrated for many decades, yet there are still enough to sow all sorts of confusion and misinformation.

The skeptic choir is preaching this typical line Arthur Rorsch issued a new report here where he specifically states

in this he states "The IPCC asserts that dangerous anthropogenic global warming (DAGW) is occurring, and that this is caused by the accumulation of human-related CO2 in the atmosphere. As yet, however, no indisputable scientific proof, or even strong empirical evidence, has been provided for such an effect, which therefore remains a matter of speculation."

Two of the 10 human fingerprints in the first link show increased downwelling longwave radiation and reduced outgoing longwave radiation at GHG-specific wavelengths, which are direct observations of the enhanced greenhouse effect. Skeptics don't mention them too much...

That if you reduce the escape of heat, but do not reduce the incoming heat, things warm up;

That the atmosphere contains molecules that absorb Infra-Red radiation;

That radiated energy depends on the temperature of the radiating object; and

That the atmosphere gets cooler as you get higher, so that the Infra-Red absorbing molecules in the atmosphere radiate less energy to space than they absorb from the surface.

I already understood 1 and 2 and thought that was the whole story, but your 3 and 4 left me a tiny bit confused.

Given the system is in equilibrium and has a top-of-atmosphere temperature T0, emitted radiation will be a quantity that can be calculated, say R0. If the result of incoming solar radiation is a surface temperature T1 and the top of atmosphere temperature remains at T0 (ie unable to radiate any more that R0), then the effect will be to change the atmospheric temperature by T1-T0. As the atmosphere is now warmer, the difference between that and the surface is reduced, so the surface stays warmer as well. This is what I understand to be the greenhouse warming effect.

What I am missing is why the top of atmosphere does not warm as well, thus radiating more heat into space. Is it because the greenhouse gasses are physically trapping the heat from the surface and preventing it from reaching the TOA? At some point, surely the incoming and outgoing radiation must balance, or we would be living on a cinder. Is this where I am missing something?

I can see that the lapse rate means the upper atmosphere is always colder than the lower atmosphere, but given an increase of 1 degree in T1, why does T0 not eventually rise by 1 degree as well, to balance the energy in the system? Or does T0 eventually increase and that becomes the new equilibrium temperature?

Sorry if these are dumb questions, but my physics knowledge could be written on the back of a postage stamp and I am really interested in understanding.

owl905 @ 20, Thanks for the reply. I think the penny has dropped: For a given stable level of insolation and a given level of CO2, the surface temperature will be a constant inversely related to the temperature at the top of atmosphere. The radiation at TOA plus the energy of the heat trapped near the surface equals the energy provided by the insolation. By adding CO2, we are keeping constant insolation, but trapping more heat near the surface, so the TOA becomes cooler, to keep my equation in balance. So, for any increase in CO2, we will see TOA cooling and surface warming, but the whole equation remaining in balance. Have I understood correctly?

"There were comments at this site some time ago (too long for me to find them now) that led me to believe that increasing the CO2 content of the atmosphere raises the average altitude from which IR radiation escaped to space. Ever since that time I have wondered how that works (if true), and your post has stimulated me to ask."

Yes, when you add more CO2 the average altitude at which IR is able to escape to space does increase. But it is more complicated (and more interesting) than that.

Whether IR can escape to space requires that the amount of GH gases above it is low enough that the probability of it being absorbed by those molecules drops to something significantly below 100% And this probability depends on 2 things. How many GH molecules are between the IR photon and Space and the probability that the GH molecule will absorb it if they happen to interact. No GH molecule will automatically absorb an IR photon that passes close enough to it. There is a certain probability that it will. And this probability isn't constant across the entire frequency range that a GH molecule can absorb at. It is more likely at some frequencies than others.

So the altitude at which escape to space is possible varies with frequency. At frequency f1, the probability of a CO2 molecule absorbing a photon at frequncy f1 mght be X. At frequency f2, if CO2's probability of absorbing at f2 is X/2, then there need to be twice as many CO2 molecules available to give the same effective probability of absorption. So the altitude at which f2 photons have a clear path to space is lower than the altitude for f1 photons.

And this behaviour is clearly visible in the graph's Tom has put up. But to understand this we need some extra information. What the temperature profile of the atmosphere is like. As we rise from the ground, air temps drop by around 6.f DegC / km. This keeps happening for between 11-17 kilometers, depending on what latitude you are at. Then as you go higher temperatures don't drop any further. This point is called the Tropopause and is the dividing point between the Troposphere and the Stratosphere. Then as you go higher into the Stratosphere temperatues don't change for quite some period. Then in the upper Stratosphere temps actually start to warm again.

And we can see exactly this in the Graph. CO2 has a distribution of absorption probabilities that is highest at the centre of the notch and declines fairly linearly as we move to frequencies on either side. Notice the spike at the centre of the CO2 notch. This is the frequency where CO2 is most likely to absorb. It is so likely that the altitude at which the path to space for that central frequency is in the upper stratosphere where temps are somewhat warmer. Then as we run our eye slowly to the left from that central spike the intensity drops. That is us moving down through the upper Stratosphere and temps are getting colder. Then the spike reaches the 220K line on the graph and roughly stays there as we keep moving out. At this point our decrease in altitude has taken us into the lower Stratosphere where temperatures don't change evean as our clear to space altitude keeps dropping. Finally as we move further out the IR line starts to climb again, to warmer values. Now we are descending even lower, below the Stratosphere into the Troposphere and we are seeing it's temperature profile as we descend further.

Eventually, the CO2 notch meets the region on the left that is all 'ragged'. This is H2O absorption lower in the Troposphere. This doesn't mean that CO2 still plays no part. Rather its probability of absorption is now so low, its clear to space altitude is so low, that even if an IR photon could get past all the CO2 molecules, the probabilty of being absorbed by H2O molecules means they still can't escape. So here H2O's behaviour dominates.

If you keep coming back from time to time, I intend to put a post up here at SkS sometime in the next 2 weeks that will go into all this in some detail, including graphics that will make it a lot easier to understand than just words.

@Doug 21 - decent summary, same page as you. The balance is restored after the change in GHG's levels out ('in the pipe' lag). In a picture of the heat balance, allow for absorption by land and water. Another fly in the ointment is the cooling effect from upper atmosphere ozone (the CFC issue).

These may be a dumb questions but on the Conrath Graph, at 975 cm^-1,interpolation between 280K and 300K give a temperature of 294.5K. Isn't this significantly higher than the measured temperature at the earth surface? And couldn't it signify that some of the absorbed radiation is emitted at this wave number?

dunc461 @25, around 295 K (23 degrees C) is a reasonable estimate of the surface temperature based on the Conrath data. Of course, the Earth's Mean Global Surface Temperature is about 288 K (15 C), however, that is the mean temperature, not the temperature at any given location. The observations in this case were made over the Gulf of Mexico near Brownesville, Texas, so a surface temperature around 23 C is hardly surprising.

Thanks to everyone who responded to my inquiry! I'm an oceanographer and can hold my own on most discussions of carbon in the ocean, but the processes that influence the radiation balance in the atmosphere remain a challenge. Consequently, I appreciate the opportunity provided by SkS to learn about climate-related processes outside my own field.

Steve Case @1, the scarey thing is I'm encountering an increasing number of people in Canada who seem to doubt the existence of even the greenhouse effect. The far-reaching disinformation campaign seems to be muddying the waters rather effectively. In light of this, I feel its the duty of the choir to sing loudly to bring sanity back to this (should be) non-debate

@28- This is not being helped by the latest news re this year's proposed budget in Canada. From our local newspaper;"The federal Conservatives are planning significant spending cuts for the upcoming 2012-13 budget years in areas such as environmental monitoring, fisheries and oceans, Via Rail, national defence, the Canadian Space agency and green energy initiatives." The budget, according to the report, will cut funding to the Canadian Environmental Agency by 43%. (Edmonton Journal February 29th) And, of course, Canada pulled out of Kyoto earlier this year.

@jimb 29 and DMCarey 28 - DM's fear is warranted. It's sanctified by the National Post, upheld by most of the other 'national' newspapers. And a decade of national governance that's power-base is built on the tar pits has taken the old phrase 'blue-eyed Arabs' to a whole new level.

Boba10960, Strong second on the critical value of this explanation. I have been studying ths subject for some time, and most discussion gloss over this as if everybody knows it. But we don't we just assume someone did thier work and so we can just wave our arms as the article sais to communicate. I am mostly an avid arm-waver; who knows it might help to cool the planet.
Like so many ither posts here, this is really valuable instruction.
A hardy thanks to all who work so hard to provide such good stuff.

incoming solar radiation is ~341.3 W/m2, of which ~101.9 is immediately reflected back out into space. 0.9 W/m2 is estimated to be absorbed by the oceans. The outgoing LWR is 238.5 W/m2.
I'm not too good at math, but 238.5 + 101.9 + 0.9 = 341.3, which basically tells me that, at least to the first decimal place, the energy balances... which is pretty much what I expected, based upon certain principles of thermodynamics.

It was my impression that the greenhouse effect was due to a slowing of the escape of outgoing heat by its absorption and re-emission (so-called radiative heat transfer) by GHGs. The increased heat is manifested as a higher temperature, owing to a certain other principle of thermodynamics. It has been my understanding that the outgoing long-wave radiation is suppressed in the absorption bands for GHGs--a telltale sign that GHG warming is occurring--but that owing to the increase in temperature (due to greenhouse warming), the emission in the parts of the spectrum transparent to outgoing longwave radiation is increased.
Either my understanding is wrong, or the excerpted statement is wrong. Someone please correct me. (I can take it.)

Your understanding is quite good. The statement you quote above is not wrong either, though it could be modified to be made more clear that it refers to the instantaneous effect of adding GHG's and not the final effect. The apparent contradiction can be resolved if you interrogate more closely the steps going from perturbation to equilibrium:

1) Suppose first we introduce some extra CO2 into the atmosphere while holding temperature fixed. This is the step where the outgoing radiation to space is reduced. The consequence of this is that if we leave the incoming solar radiation unchanged, more energy is coming into the planet than is exiting. This is the "slowing of outgoing heat by its absorption and re-emission" that you referred to.

2) Because of this the planet warms, and the emission increases to space in order to let that imbalance decay to zero. This is the step that you are talking about.

3) When measured from space, the net result is actually that the outgoing radiation has not changed at all from the initial value once you go back to equilibrium, since it must match the unchanged solar radiation. However, changes have been in the vertical distribution of how that energy escapes. Specifically, the height of the so-called TAU=1 (an optical depth coordinate) level increases, such that the "mean" level of emission to space decreases in pressure (or increases in height). Of course, the height of this surface is really a strong function of wavelength.

Note that in my plots in the feedbacks and runaway post, I plotted OLR as a function of temperature. Thus, if you pick any specific temperature (say, 300 K) the OLR is reduced by adding CO2. Look at figure 2 for example in that post. That will always be true because of the absorption by the excess CO2. However, for thermodynamic reasons, this disequilibrium cannot be maintained forever, since it must be accompanied by an increase in temperature. So instead of thinking about the instantaneous effect of adding CO2 as decreasing the OLR for fixed T, you can think of it as increasing the temperature for a fixed equilibrium point (i.e., where the OLR intersects the incoming solar curve).

"That means that the red area itself, which is the upwards radiation from the surface minus the upward radiation to space, is the reduction in energy radiated to space because of the presence of Infra-Red absorbing molecules in the atmosphere. That is, it is the greenhouse effect."

As is evident from the initial part of the first sentence, if discusses modtran diagram above, and refers to the difference between the Infrared radiation from the surface, and the Infrared radiation to space. On Trenberth's diagram, it is the difference between the Surface Radiation (396 W/m^2) and the Outgoing Longwave Radiation (239 W/m^2). Without that difference, there would be a approximately 150 W/m^2 energy imbalance between incoming and outgoing energy which would very rapidly cool the surface to about 255 degrees K (-18 degrees C).

Except for the interpretation of what I said, there is little to disagree with in Coal Geologists explanation, and nothing in Chris Colose's. The little I disagree with is saying "...that the greenhouse effect was due to a slowing of the escape of outgoing heat by its absorption and re-emission (so-called radiative heat transfer) by GHGs." Although green house gases do increase the time it takes for energy to go from the surface to space, on average, that of itself will not cause a greenhouse effect.

owl905 @34, I'm sorry, but you have been had. The "ricochet on the pool table" is irrelevant to the greenhouse effect.

The most fundamental fact about the greenhouse effect is that if the energy escaping to space exceedsis less than the energy entering the system, then the temperature will rise until they balance again. If the energy escaping is less thanexceeds the energy entering system, temperatures will fall until they balance again.

Now, if you imagine a series of pipes, with a tap which will be used to force water flowing through the pipe to take a longer or a shorter route. If you switch from the shorter to the longer route, but maintain a constant flow, there will be no build up of pressure, and the reservoir you are draining will not drain any slower.

Analogously, if you introduced GHG to the atmosphere so that energy took longer to reach space, but maintained the same temperature at all altitudes so that the amount of energy being emitted to space was not reduce, you would not warm the surface of the planet.

The ricochet is a characteristic of the GH Effect But it isn't what defines the GH Effect. If the ricochet is what defines how long it takes a pool ball to leave the table, what is far more important is how many balls are on the table because of that. If one pool ball ricochet's off per second, so what. How many balls does it need on the table to generate that one ricochet per second.

#33 Chris : "However, changes have been in the vertical distribution of how that energy escapes. Specifically, the height of the so-called TAU=1 (an optical depth coordinate) level increases, such that the "mean" level of emission to space decreases in pressure (or increases in height)."

#36 Tom : "The most fundamental fact about the greenhouse effect is that if the energy escaping to space exceeds the energy entering the system, then the temperature will rise until they balance again."

These two comments bring me to ask a question: the system will warm, but where should it warm? By where I mean at which height? The same point than #19 Bart. It has been answered to Bart that the higher layers of atmosphere will cool rather than warm because of IR trapping near surface (so these higher layers would emit less at T^4 toward outer space). But that is unclear for me, because if we speak of a thermodynamical equilibrium, there are also non-radiative mechanisms on Earth, precisely between surface and troposphere (for example latent heat and wet convection if there is a water vapour feedback).

skept.fr @38, within the troposphere, and to a first approximation, and ignoring feedbacks, all altitudes will heat equally. Of course, with that many qualifications the answer is probably not very satisfying.

The two most important of the caveats are the spatial (within the troposphere) and the feedbacks. The consequence of increased greenhouse gases at the boundary of the troposphere (the tropopause) will be to warm the lower reaches, thereby lifting that boundary. Above that, in the stratosphere it definitely cools but the reason for the cooling is not certain, and extensively discussed elsewhere on SkS. (Hint: of topic for this thread, but you are welcome to follow the link read the comments and wade in.)

Feedback wise, the most important feature is the Lapse Rate Feedback. In the lapse rate feedback, the Lapse rate becomes smaller (smaller decrease in temperature with altitude) due to increased water vapour in the atmosphere, resulting in a warmer upper troposphere relative to the lower troposphere in areas of high humidity, ie, the tropics. Again, extensively discussed elsewhere.

All this is arm waving, so it would be better to look at the model predictions:

This however also takes us of topic. I would appreciate it if we restrict discussion of the enhanced greenhouse effect, ie, how the greenhouse effect changes with increased GHG to some other thread, or wait till I actually discuss it later in this series.

I've used a more detailed version of the 'pool balls analogy' for global warming previously. Specifically;

Imagine balls (photons) moving in a completely frictionless environment on a pool table (the Earth's atmosphere). Since there is no friction they will continue bouncing around until they hit one of the pockets (escape to space). Now assume that additional pool balls (incoming photons from sunlight) are rolled onto the table at a fixed rate. Let's also say that the size of the table and the momentum of the pool balls is such that on average balls leave the table at the same rate that they enter it. Now, if we block off one of the pockets (increase greenhouse gas levels) the balls will initially not be able to escape at the same rate and thus the incoming balls will result in an increasing number of balls on the table (more energy in the atmosphere) which results in more collisions and greater total momentum until eventually the rate of balls exiting the table again equals the rate at which they are entering... just with more balls on the table (higher atmospheric temperatures) at any given time.

Thus, no it isn't really the ricochets per se... in this simplified example warming is caused by a change in the rate at which energy escapes the system. That does result in more ricochets, but it is the temporary imbalance between incoming and outgoing rate which is the real issue.

Tom Curtis @26 Thank you for your information. I agree that a surface temperature of 23 Degrees C is hardly surprising. But http://www.nodc.noaa.gov/dsdt/cwtg/wgof.html shows water temperatures below 21.6 Degrees for 6 months out of the year. Do you happen to know when the observation was made? Or can you provide an open source of experimental data where the assumption, that all energy absorbed is emitted at the same wave number, is verified? Thanks.

1) The observations where made at 17:34 GMT (ie, 11:34 AM in Texas), on Central Time Zone April 22nd, 1969. The surface temperature was 298 K, as measured by a Nomad buoy. The reason for the slight difference between measured and brightness temperatures is that the emissivity of sea water is not exactly 1. The radiosonde data used to set up the model was recorded 100 km from the satellited observation site, and 26 minutes later.

2) As you are obviously very keen on checking the empirical validation of models, you may be interested in this data from Dessler et al, 2008, which compared Outgoing Longwave Radiation observation by the Ceres satellite with three models. The first graph shows the scatter plot of model predictions against observations for the best performed of the three models. Any point falling on the black line shows a perfect match between model and observation. Across the 134,862 observations, the match between model prediction and satellite observation is remarkable.

I really wanted to include this plot with the original article as it is far more telling than evidence than the Conrath observation that I did include. In the end, the ease of comparison between the Modtran output, the validation of the wavelength by wavelength comparison, and the need to keep the post reasonably brief mitigated against it. Never-the-less the knowledge of just one paper making comparisons of over 134 thousand observations, each proving the existence of the greenhouse effect really makes me chuckle whenever I see yet another internet blogger masquerading as a skeptic and saying that nobody has ever observed the greenhouse effect.

Caption: Figure 1. Scatterplot of 134,862 measured values of OLR against OLR calculated by the Fu-Liou model, both in units of W/m2. The solid line is the one-to-one line.

And just for good measure, here is figure 2 from the same paper, comparing accuracy of two of the models over a range of latitudes and surface temperatures. It is not just coincidence of circumstance which allows such stunning predictive accuracy.

Need I say it? Radiative transfer physics is settled science!

3) I cannot provide any experimental data showing that "... all energy absorbed is emitted at the same wave number", because the assumption is false everywhere except in lasers. More importantly, it is irrelevant because no such assumption is made either in models of radiative transfer, nor in my article.

I see nothing wrong with owl905's "pool table" analogy ( @34), as further explained by CBDunkerson ( @40). Tom Curtis's "pipe" analogy ( @36) can be reconciled with the pool table simply by coiling the pipe so that the outlets occur at the same point. If the pipes are carrying heat (and there's no internal friction), then the flow rate will be the same, yet the spatial concentration of heat will be greater in the longer coiled pipe (a hookah?) than in the shorter straight pipe (a calumet?). (With apologies to Ray Pierrehumbert and others, I like a nice, simple model much more than differential equations, though I'm glad someone can figure out the associated math!)

"Suppose somebody told us their water pump was broken, but that the Second Law of Thermodynamics prohibited transfer of heat from a cooler place (the water) to a hotter place (the engine block), so they'ld be fine so long as they didn't rev any faster than normal, we'ld look at them in complete disbelief."

Don't you mean "Suppose somebody told us their water pump was broken, but that the Second Law of Thermodynamics prohibited transfer of heat from a hotter place (the engine block) to a cooler place (the water)"?

skymccain @47, not it is correct as written. In that form it exactly mirrors a common so-called climate skeptic argument. The argument made is that heat cannot flow from a cooler to a warmer location, and that therefore back radiation from the atmosphere (which is admittedly cooler than the surface) cannot result in the surface being warmer.

In the analogy, the "mechanical breakdown skeptic" claims that the cool water cannot transfer heat to the warm engine block, so that even if the water gets warmer because of the broken pump, it will still be cooler than the engine block and therefore not capable of warming it. The presumed consequence is that the engine will therefore not run hotter because of a faulty water pump.

Of course, nobody (or at least nobody sane) would run that argument about cars. But we are repeatedly challenged by so-called skeptics who have incontrovertible proof that "global warming is a lie", where the "proof" turns out be nothing more than the obviously false engine block argument transposed to the atmosphere. As of today, the thread I linked to has 1393 comment from repeated attempts by so-called skeptics to disprove fundamental laws of physics, and patient attempts to show them what is wrong with the argument.

Tom Curtis @43
Thanks again for your response and patience. My concern is not with the accuracy of the models but in trying to understand the process. Somewhere I picked up the concept that the greenhouse effect was caused by the absorption by certain gases of energy radiating from the earth’s surface at specific wave lengths and re-emitting that energy at the same wavelengths, but in all directions so that half of the energy re-emitted is directed back towards earth. This seem plausible to me because if the energy were re-emitted at whole range of wavelengths, some of the energy would be re-emitted in the “transparent windows” and the energy measured, at the top of the atmosphere, in those windows, would be greater than a Black Body Radiation Calculation would predict. Your answer seems to rule out both possibilities so I guess the entire concept is invalid. I apologize for bothering you with my stupid questions.

Case 1: Suppose you have a planet which is a perfect black body, and perfectly conductive. Therefore, the outgoing radiation from the surface of the planet will equal the incoming insolation, and the surface temperature, T, will be

(a) T = (I/4s)^0.25, where "I" is the incoming insolation and "s" is the Stefan Boltzmann constant.

Case 2: Suppose we have instead the same planet, but now cloaked in an atmosphere which is perfectly absorbing (and emitting) wavelengths. In this case the atmosphere's temperature will be given by equation (a). In this case, because the atmosphere radiates equally up and down, initially it will be cooler, but as the surface warms beneath it, the upward radiation from the surface will rise to match the downward radiation from the atmosphere until both equal the incoming solar radiation. So the temperature of both atmosphere and surface will be given by the equation:

Note that in case (2), there is a lot more "pool table ricochets", but the temperature is not increased relative to case (1). Therefore increasing the time it takes for radiation to escape to space is not a sufficient condition to establish a green house effect.

I have, of course used a slab model for this discussion, which is inaccurate in life, but allows clarity in seeing the relevant relationships.